Many problems encountered in the fields of
engineering, physics, mathematics, and e.t.c. can be described by differential equations.
For example, differential equations are used in
the simulation of oscillation phenomena [1]}, the social sciences [2]},
the treatment of tumors [3]}, and e.t.c..
In many cases, problems are expressed in the form of the
higher-order and the non-linear ordinary differential equations.
For example, a high-order differential equation filter can effectively
remove the noise in a signal [4]}.
However, to analytically solve the ordinary differential
equations (ODEs), especially the higher-order and the non-linear ODEs, is difficult.
For example, the analytical methods such as
the series method [5]}, [6]}
and the constant-transform method [5]}
sometimes fail at the higher-order and the non-linear cases.
